Survival and complete convergence for a spatial branching system with local regulation
- Birkner, Matthias
- Depperschmidt, Andrej
2010 Mathematics Subject Classification
- 60K35 92D40
- Regulated population, survival, coexistence, complete convergence
We study a discrete time spatial branching system on $Z^d$ with logistic-type local regulation at each deme depending on a weighted average of the population in neighbouring demes. We show that the system survives for all time with positive probability if the competition term is small enough. For a restricted set of parameter values, we also obtain uniqueness of the non-trivial equilibrium and complete convergence, as well as long-term coexistence in a related two-type model.
- Ann. Probab., 17 (2007) pp. 1777-1807.